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arXiv · 1809.05975

Graphs with no $K_9^=$ minor are 10-colorable

Martin Rolek
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Abstract

Hadwiger's conjecture claims that any graph with no $K_t$ minor is $(t - 1)$-colorable. This has been proved for $t \le 6$, but remains open for $t \ge 7$. As a variant of this conjecture, graphs with no $K_t^=$ minor have been considered, where $K_t^=$ denotes the complete graph with two edges removed. It has been shown that graphs with no $K_t^=$ minor are $(2t - 8)$-colorable for $t \in \{7, 8\}$. In this paper, we extend this result to the case $t = 9$ and show that graphs with no $K_9^=$ minor are $10$-colorable.

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Martin Rolek. 2018-09-16. Graphs with no $K_9^=$ minor are 10-colorable. https://arxiv.org/abs/1809.05975

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